correctness / propriety
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correctness
The quality of being free from errors; the correctness or accuracy of information, calculations, or statements.
Der Lehrer überprüfte die Korrektheit der mathematischen Lösungen.
The teacher checked the correctness of the mathematical solutions.
The noun 'Korrektheit' (correctness/propriety) is derived from the adjective 'korrekt' (correct). The ending '-heit' forms an abstract feminine noun that describes the state or quality of being correct.
Die Korrektheit seiner Argumentation wurde von niemandem bezweifelt.
The correctness of his reasoning was doubted by no one.
To express what the correctness refers to, German often uses the genitive or the preposition 'von' (+ dative). Typical verbs in this context are 'prüfen' (to check) or 'bestätigen' (to confirm).
Bitte überprüfen Sie die Korrektheit der Lieferadresse.
Please check the correctness of the delivery address.
In the meaning of social behavior, 'Korrektheit' (propriety/correctness) is very often used in the fixed expression 'politische Korrektheit' (political correctness). This refers to the careful use of language in order not to discriminate against anyone.
Die Debatte über politische Korrektheit wird oft sehr emotional geführt.
The debate about political correctness is often very emotional.
You can recognize the meaning from the context: If it is about facts, numbers, or grammar, correctness is meant. If it is about social behavior, decency, or language in public spaces, the social norm is often meant.
Die Korrektheit des Ergebnisses muss noch bestätigt werden.
The correctness of the result still has to be confirmed.
decency / hesitation
'der Anstand' and 'die Korrektheit' can both describe someone behaving appropriately and respectfully. 'Anstand' sounds more personal and means a sense of good manners and consideration. 'Korrektheit' sounds more formal and emphasizes that someone follows rules and social norms. In private situations, 'Anstand' is often more natural. In official or very formal situations, 'Korrektheit' can be more precise because it sounds more strongly connected to rules and order.
Bei der Begrüßung der Gäste achtete sie auf höfliche Korrektheit.
When greeting the guests, she paid attention to polite propriety.
Im Restaurant ist es eine Frage des Anstands, freundlich mit dem Personal zu sprechen.
In a restaurant, it is a matter of decency to speak politely to the staff.